Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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ciei occurrens in
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K
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&
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L.
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Et velocitas aquæ effluentis per fora
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men
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EF
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ea erit quam aqua cadendo ab
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I
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& caſu ſuo deſcribendo
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altitudinem
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IG
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acquirere poteſt. </
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>Ideoque per Theoremata
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Galilæi
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erit
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ad
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IH
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in duplicata ratione velocitatis aquæ per foramen
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effluentis ad velocitatem aquæ in circulo
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AB,
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hoc eſt, in dupli
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cata ratione circuli
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AB
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ad circulum
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EF
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; nam hi circuli ſunt re
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ciproce ut velocitates aquarum quæ per ipſos, eodem tempore &
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æquali quantitate, adæquate tranſeunt. </
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>De velocitate aquæ hori
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zontem verſus hic agitur. </
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>Et motus horizonti parallelus quo par
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tes aquæ cadentis ad invicem accedunt, cum non oriatur a gravi
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tate, nec motum horizonti perpendicularem à gravitate oriundum
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mutet, hic non conſideratur. </
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>Supponimus quidem quod partes
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aquæ aliquantulum cohærent, & per cohæſionem ſuam inter ca
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dendum accedant ad invicem per motus horizonti parallelos, ut
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unicam tantum efforment cataractam & non in plures cataractas
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dividantur: ſed motum horizonti parallelum, a cohæſione illa ori
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undum, hic non conſideramus.
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DE MOTU
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CORPORUM</
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Cas.
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1. Concipe jam cavitatem totam in vaſe, in circuitu aquæ
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cadentis
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ABNFEM,
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glacie plenam eſſe, ut aqua per glaciem
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tanquam per infundibulum tranſeat. </
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>Et ſi aqua glaciem tantum
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non tangat vel, quod perinde eſt, ſi tangat & per glaciem propter
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ſummam ejus polituram quam liberrime & ſine omni reſiſtentia la
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batur; hæc defluet per foramen
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EF
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eadem velocitate ac prius, &
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pondus totum columnæ aquæ
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ABNFEM
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impendetur in deflu
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xum ejus generandum uti prius, & fundum vaſis ſuſtinebit pon
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dus glaciei columnam ambientis.
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<
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>Liqueſcat jam glacies in vaſe; & effluxus aquæ quoad velocita
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tem, idem manebit ac prius. </
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>Non minor erit, quia glacies in aquam
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reſoluta conabitur deſcendere: non major, quia glacies in aquam
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reſoluta non poteſt deſcendere niſi impediendo deſcenſum aquæ
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alterius deſcenſui ſuo æqualem. </
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>Eadem vis eandem aquæ effluen
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tis velocitatem generare debet.
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<
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>Sed foramen in fundo vaſis, propter obliquos motus particula
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rum aquæ effluentis, paulo majus eſſe debet quam prius. </
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ticulæ aquæ jam non tranſeunt omnes per foramen perpendicula
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riter; ſed a lateribus vaſis undique confluentes & in foramen con
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vergentes, obliquis tranſeunt motibus; & curſum ſuum deorſum
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flectentes in venam aquæ exilientis conſpirant, quæ exilior eſt pau
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lo infra foramen quam in ipſo foramine, exiſtente ejus diametro
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ad diametrum foraminis ut 5 ad 6, vel 5 1/2 ad 6 1/2 quam proxime, ſi </
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